The number of franchises that Barry will open each year in year 5, year 14, and year 26 will be 45, 90, and 150.
a = 25
d = 5
The fifth year will be:
= a + (n - 1)d
= 25 + (5 - 1)5
= 25 + (4 × 5)
= 45
The 14th year will be:
= a + 13d
= 25 + 13(5)
= 90
The 26th will be:
= a + 25d
= 25 + 25(5)
= 150
The total franchises Barry’s will have in operation in year 10, year 22, and in year 50 will be:
Year 10 = n/2[2a + (n - 1)d]
= 10/2[5(25) + 45]
= 475
Year 22 = 25[50 + 245]
= 1705
Year 50 = 25(50 + 245)
= 7375
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